A binary signal can represent one of two possible states, called 0 and 1. A set of n binary signals can represent 2n states. An n-bit bus comprises n wires that are used to transmit n binary signals between two elements of a system. An n-bit memory location is used to store an n-bit binary state.
In a computer system, the size of the memory is limited by the number of bits that can be put into a predetermined area. The size of a bus in the system is limited by one of two things:                1) the number of physical pins that can be put into a predetermined area, or 2) the number of drivers that can be switched simultaneously without creating more noise than can be safely tolerated by the system.        
In any computer system, it is desirable to have the memory be as large as possible, and the busses be as wide as possible. Since the number of memory cells and the number of wires in a bus are fundamentally limited as stated above, it is clearly useful to use those memory cells and wires to carry more information in some way.
There has been much research to date in which ternary (3-state) signals are the basis for state representation. A ternary signal can represent one of three possible states, called 0, 1, and 2. A set of n ternary signals can represent 3n states. Very clearly, in a ternary system, more information can be stored/transmitted per cell/wire than in a binary system.
There are numerous problems, however, with the practical implementation of a ternary system, some of which are described below. Nonetheless, the plethora of interest in ternary systems clearly demonstrates the perceived usefulness of being able to represent more than binary states in a fixed number of cells or wires.